The New College of the Humanities is looking to gain its own degree-awarding powers and expand overseas if its London campus is a success.
A.C. Grayling's private liberal arts institution, which charges undergraduates ?18,000 a year, hopes to confer its own degrees within three to four years, Times Higher Education understands.
Currently, students follow University of London degrees, but also study modules in areas such as applied ethics and science literacy.
In some subjects, academics at the college are frustrated at having to teach another institution's programme, it is understood.
David Willetts, the universities and science minister, welcomed the announcement in July that the private, charitable Regent's College had won degree-awarding powers, a move he said would encourage greater competition in the sector.
At present, only six private providers have degree-awarding powers. The powers are granted by the Privy Council on the advice of the Quality Assurance Agency, which looks for a "well-founded, cohesive and self-critical academic community that demonstrates firm guardianship of its standards".
Sixty students have enrolled at NCH this year, after Professor Grayling's early estimates of an initial intake of 180 to 200.
It is understood that other members of the college's senior management did not think the target was realistic.
NCH, which has a for-profit parent company, accepted students with average A-level grades of A*AA.
It decided not to boost numbers by lowering its offer during clearing in order to protect its reputation.
It is also understood that the college would consider establishing other campuses across the world if its London venture is successful.
As reported by THE in April, the institution's founders had considered setting up in Asia rather than the UK. The UK's hostility to innovation and its "tall poppy syndrome" had prompted second thoughts about setting up in London.
Thomas Docherty, professor of English and comparative literature at the University of Warwick, said that it was "not surprising that NCH is trying to get degree-awarding powers; the disgrace and further betrayal of the UK HE sector will be if they are allowed to have them".
Professor Docherty, a prominent critic of the college, said that it had "failed to recruit what would constitute the number of students that is normally required to run a module in any existing UK degree programme".
The college did not respond to THE's request for comment.